1 answer

A Simple Gear System

Question:

Gears are important components inmany mechanical devices, from mechanical clocks to bicycles. Infact, they are present whenever a motor produces rotationalmotion.An example of a simple gear systemis shown in the figure.The bigger wheel (wheel 1) hasradius r_1, while the smaller one (wheel 2) has radius r_2. The two wheels have small teeth and are connectedthrough a metal chain so that when wheel 1rotates, the chain moveswith it and causes wheel 2 to rotate as well.
intro1intro21011362A.jpg1.)Let wheel 1 rotate at a constant angularspeed omega_1. Find the ratio frac{omega_1}{omega_2} of the angular speed of wheel 1 to theangularspeed of wheel 2.Express your answer in terms of anyor all of the variables r_1 and r_2. frac{omega_1}{omega_2}= ?2.) The rotation of wheel 1 is caused by atorque tau_1. Find the ratio frac{tau_1}{tau_2} of the torque acting on wheel 1 to thetorqueacting on wheel 2.Express your answer in terms of anyor all of the variables r_1 and r_2.frac{tau_1}{tau_2}= ?3.)If the power needed to rotate wheel 1 isP_1, whatis the ratio  frac{P_1}{P_2}of the power of wheel 1 to the power of wheel2?Express your answer in terms of anyor all of the variables r_1 and r_2. frac{P_1}{P_2}= ?

Answers

For #1, i think the ratio is 1, because they move the same amountradians, if not the chain would not spin equally around thecycle!
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